{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T22:55:14Z","timestamp":1778712914750,"version":"3.51.4"},"reference-count":53,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,6,17]],"date-time":"2021-06-17T00:00:00Z","timestamp":1623888000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In the area of musculoskeletal MR images analysis, the image denoising plays an important role in enhancing the spatial image area for further processing. Recent studies have shown that non-local means (NLM) methods appear to be more effective and robust when compared with conventional local statistical filters, including median or average filters, when Rician noise is presented. A significant limitation of NLM is the fact that thy have the tendency to suppress tiny objects, which may represent clinically important information. For this reason, we provide an extensive quantitative and objective analysis of a novel NLM algorithm, taking advantage of pixel and patch similarity information with the optimization procedure for optimal filter parameters selection to demonstrate a higher robustness and effectivity, when comparing with NLM and conventional local means methods, including average and median filters. We provide extensive testing on variable noise generators with dynamical noise intensity to objectively demonstrate the robustness of the method in a noisy environment, which simulates relevant, variable and real conditions. This work also objectively evaluates the potential and benefits of the application of NLM filters in contrast to conventional local-mean filters. The final part of the analysis is focused on the segmentation performance when an NLM filter is applied. This analysis demonstrates a better performance of tissue identification with the application of smoothing procedure under worsening image conditions.<\/jats:p>","DOI":"10.3390\/s21124161","type":"journal-article","created":{"date-parts":[[2021,6,17]],"date-time":"2021-06-17T11:20:26Z","timestamp":1623928826000},"page":"4161","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Quantitative and Comparative Analysis of Effectivity and Robustness for Enhanced and Optimized Non-Local Mean Filter Combining Pixel and Patch Information on MR Images of Musculoskeletal System"],"prefix":"10.3390","volume":"21","author":[{"given":"Jan","family":"Kubicek","sequence":"first","affiliation":[{"name":"Department of Cybernetics and Biomedical Engineering, VSB\u2013Technical University of Ostrava, 17. listopadu 15, 70800 Ostrava Poruba, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michal","family":"Strycek","sequence":"additional","affiliation":[{"name":"Department of Cybernetics and Biomedical Engineering, VSB\u2013Technical University of Ostrava, 17. listopadu 15, 70800 Ostrava Poruba, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8893-2587","authenticated-orcid":false,"given":"Martin","family":"Cerny","sequence":"additional","affiliation":[{"name":"Department of Cybernetics and Biomedical Engineering, VSB\u2013Technical University of Ostrava, 17. listopadu 15, 70800 Ostrava Poruba, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9527-4642","authenticated-orcid":false,"given":"Marek","family":"Penhaker","sequence":"additional","affiliation":[{"name":"Department of Cybernetics and Biomedical Engineering, VSB\u2013Technical University of Ostrava, 17. listopadu 15, 70800 Ostrava Poruba, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ondrej","family":"Prokop","sequence":"additional","affiliation":[{"name":"MEDIN, a.s., Vlachovicka 619, 59231 Nove Mesto na Morave, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3781-1280","authenticated-orcid":false,"given":"Dominik","family":"Vilimek","sequence":"additional","affiliation":[{"name":"Department of Cybernetics and Biomedical Engineering, VSB\u2013Technical University of Ostrava, 17. listopadu 15, 70800 Ostrava Poruba, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"104732","DOI":"10.1016\/j.ijrmms.2021.104732","article-title":"A novel approach for fracture skeleton extraction from rock surface images","volume":"142","author":"Tang","year":"2021","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"102560","DOI":"10.1016\/j.bspc.2021.102560","article-title":"A method to improve the computational efficiency of the Chan-Vese model for the segmentation of ultrasound images","volume":"67","author":"Ramu","year":"2021","journal-title":"Biomed. Signal Process. Control."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"110186","DOI":"10.1016\/j.jbiomech.2020.110186","article-title":"Automatic generation of personalised skeletal models of the lower limb from three-dimensional bone geometries","volume":"116","author":"Modenese","year":"2021","journal-title":"J. Biomech."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"615","DOI":"10.1002\/mrm.28453","article-title":"Estimating vertebral bone marrow fat unsaturation based on short-TE STEAM MRS","volume":"85","author":"Ruschke","year":"2021","journal-title":"Magn. Reson. Med."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"025002","DOI":"10.1088\/2057-1976\/abd3de","article-title":"Automated measurements of morphological parameters of muscles and tendons","volume":"7","author":"Jabbar","year":"2020","journal-title":"Biomed. Phys. Eng. Express"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"30","DOI":"10.14366\/usg.20080","article-title":"Artificial intelligence in musculoskeletal ultrasound imaging","volume":"40","author":"Shin","year":"2021","journal-title":"Ultrasonography"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Janumala, T., and Ramesh, K.B. (2020). Development of an Algorithm for Vertebrae Identification Using Speeded up Robost Features (SURF) Technique in Scoliosis X-Ray Images. Advances in Intelligent Systems and Computing, Springer Science and Business Media LLC.","DOI":"10.1007\/978-3-030-51859-2_6"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2748","DOI":"10.1016\/j.injury.2020.09.019","article-title":"Musculoskeletal trauma imaging in the era of novel molecular methods and artificial intelligence","volume":"51","author":"Klontzas","year":"2020","journal-title":"Injury"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Sukhavasi, S., Sukhavasi, S., Elleithy, K., Abuzneid, S., and Elleithy, A. (2021). Human Body-Related Disease Diagnosis Systems Using CMOS Image Sensors: A Systematic Review. Sensors, 21.","DOI":"10.3390\/s21062098"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Moran, M., Faria, M., Giraldi, G., Bastos, L., and Conci, A. (2021). Do Radiographic Assessments of Periodontal Bone Loss Improve with Deep Learning Methods for Enhanced Image Resolution?. Sensors, 21.","DOI":"10.3390\/s21062013"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/j.neuroimage.2017.12.021","article-title":"Structural network differences in chronic musk-uloskeletal pain: Beyond fractional anisotropy","volume":"182","author":"Bishop","year":"2018","journal-title":"NeuroImage"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Roemer, F.W., Aydemir, A., Lohmander, L.S., Crema, M.D., Marra, M.D., Muurahainen, N., Felson, D.T., Eckstein, F., and Guermazi, A. (2016). Structural effects of sprifermin in knee osteoarthritis: A post-hoc analysis on cartilage and non-cartilaginous tissue alterations in a randomized controlled trial. BMC Musculoskelet. Disord., 17.","DOI":"10.1186\/s12891-016-1128-2"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1298","DOI":"10.1007\/s00330-006-0184-7","article-title":"Muskuloskeletal MR imaging at 3.0 T: Current status and future perspectives","volume":"16","author":"Bolog","year":"2006","journal-title":"Eur. Radiol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1016\/j.berh.2004.07.001","article-title":"New developments in imaging for diagnosis and therapy monitoring in rheumatic diseases","volume":"18","author":"Manger","year":"2004","journal-title":"Best Pr. Res. Clin. Rheumatol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-021-84591-1","article-title":"The magnetic resonance imaging evaluation of condylar new bone remodeling after Yang\u2019s TMJ arthroscopic surgery","volume":"11","author":"Dong","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Cao, L., Wen, J.-X., Han, S.-M., Wu, H.-Z., Peng, Z.-G., Yu, B.-H., Zhong, Z.-W., Sun, T., Wu, W.-J., and Gao, B.-L. (2021). Imaging fea-tures of hemangioma in long tubular bones. BMC Musculoskelet. Disord., 22.","DOI":"10.1186\/s12891-020-03882-2"},{"key":"ref_17","first-page":"1","article-title":"Comparison of three treatment methods for simple bone cyst in children","volume":"22","author":"Zhang","year":"2021","journal-title":"BMC Musculoskelet. Disord."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13244-020-00958-4","article-title":"CT angiography and MRI of hand vascular lesions: Technical considerations and spectrum of imaging findings","volume":"12","author":"Blum","year":"2021","journal-title":"Insights Imaging"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"6957","DOI":"10.3390\/s130606957","article-title":"In Vivo X-Ray Computed Tomographic Imaging of Soft Tissue with Native, Intravenous, or Oral Contrast","volume":"13","author":"Wathen","year":"2013","journal-title":"Sensors"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Sharon, H., Elamvazuthi, I., Lu, C.-K., Parasuraman, S., and Natarajan, E. (2019). Development of Rheumatoid Arthritis Classification from Electronic Image Sensor Using Ensemble Method. Sensors, 20.","DOI":"10.3390\/s20010167"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"7940","DOI":"10.3390\/s140507940","article-title":"Simultaneous Magnetic Resonance Imaging and Consolidation Measurement of Articular Cartilage","volume":"14","author":"Wellard","year":"2014","journal-title":"Sensors"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3479","DOI":"10.1002\/mrm.28676","article-title":"Evaluation of a similarity anisotropic diffusion denoising approach for improving in vivo CEST-MRI tumor pH imaging","volume":"85","author":"Romdhane","year":"2021","journal-title":"Magn. Reson. Med."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1007\/s10916-020-01696-2","article-title":"Rician Denoising Based on Correlated Local Features LMMSE Approach","volume":"45","author":"Kinani","year":"2021","journal-title":"J. Med Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"14","DOI":"10.4018\/JITR.2020100102","article-title":"Discrete Total Variation-Based Non-Local Means Filter for Denoising Magnetic Resonance Images","volume":"13","author":"Joshi","year":"2020","journal-title":"J. Inf. Technol. Res."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Mehmood, R., and Kaur, A. (2020, January 1\u20133). Modified Difference Squared Image Based Non Local Means Filter. Proceedings of the 2020 11th International Conference on Computing, Communication and Networking Technologies (ICCCNT), Kharagpur, India.","DOI":"10.1109\/ICCCNT49239.2020.9225284"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1504\/IJBET.2020.105652","article-title":"Edge preserving de-noising method for efficient segmentation of cochlear nerve by magnet-ic resonance imaging","volume":"32","author":"Jeevakala","year":"2020","journal-title":"Int. J. Biomed. Eng. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1523","DOI":"10.13005\/bpj\/2026","article-title":"Multimodal Image Fusion of Magnetic Resonance and Computed Tomography Brain Images\u2014A New Approach","volume":"13","author":"Chandrashekar","year":"2020","journal-title":"Biomed. Pharmacol. J."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1007\/978-981-13-9042-5_66","article-title":"An Improved Non-local Means Denoising Technique for Brain MRI","volume":"999","author":"Sarkar","year":"2020","journal-title":"Adv. Intell. Syst. Comput."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Zhu, M., Hu, Y., Yu, J., He, B., and Liu, J. (2021). Find Outliers of Image Edge Consistency by Weighted Local Linear Regression with Equality Constraints. Sensors, 21.","DOI":"10.3390\/s21072563"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Ahmed, A., Jalal, A., and Kim, K. (2020). A novel statistical method for scene classification based on multi-object categorization and lo-gistic regression. Sensors, 20.","DOI":"10.3390\/s20143871"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Liu, N., and Schumacher, T. (2020). Improved Denoising of Structural Vibration Data Employing Bilateral Filtering. Sensors, 20.","DOI":"10.3390\/s20051423"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.mri.2018.08.006","article-title":"A correlative study between diffusion and perfusion MR imaging parameters on peripheral arterial disease data","volume":"55","author":"Ioannidis","year":"2019","journal-title":"Magn. Reson. Imaging"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Mehranian, A., Belzunce, M.A., McGinnity, C.J., Prieto, C., Hammers, A., and Reader, A.J. (2017, January 21\u201328). Multi-modal weighted quadratic pri-ors for robust intensity independent synergistic PET-MR reconstruction. Proceedings of the 2017 IEEE Nuclear Science Symposium and Medical Imaging Conference, Atlanta, GA, USA.","DOI":"10.1109\/NSSMIC.2017.8532820"},{"key":"ref_34","first-page":"71","article-title":"Fast Global Image Denoising Algorithm on the Basis of Nonstationary Gamma-Normal Statistical Model","volume":"542","author":"Gracheva","year":"2015","journal-title":"Commun. Comput. Inf. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"013013","DOI":"10.1117\/1.JEI.30.1.013013","article-title":"Static\/dynamic filter with nonlocal regularizer","volume":"30","author":"Xing","year":"2021","journal-title":"J. Electron. Imaging"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Cai, S., Kang, Z., Yang, M., Xiong, X., Peng, C., and Xiao, M. (2018). Image Denoising via Improved Dictionary Learning with Global Structure and Local Similarity Preservations. Symmetry, 10.","DOI":"10.3390\/sym10050167"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"225019","DOI":"10.1088\/1361-6560\/abb71b","article-title":"A new approach to radiochromic film dosimetry based on non-local means","volume":"65","year":"2020","journal-title":"Phys. Med. Biol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"117946","DOI":"10.1016\/j.neuroimage.2021.117946","article-title":"Improved cortical surface recon-struction using sub-millimeter resolution MPRAGE by image denoising","volume":"233","author":"Tian","year":"2021","journal-title":"NeuroImage"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1007\/s12149-020-01550-y","article-title":"Non-local mean denoising using multiple PET reconstructions","volume":"35","author":"Arabi","year":"2021","journal-title":"Ann. Nucl. Med."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Heo, Y.-C., Kim, K., and Lee, Y. (2020). Image Denoising Using Non-Local Means (NLM) Approach in Magnetic Resonance (MR) Imaging: A Systematic Review. Appl. Sci., 10.","DOI":"10.3390\/app10207028"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"184866","DOI":"10.1109\/ACCESS.2020.3029297","article-title":"Anisotropic Weighted KS-NLM Filter for Noise Reduction in MRI","volume":"8","author":"Kanoun","year":"2020","journal-title":"IEEE Access"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2838","DOI":"10.1109\/TMI.2019.2915629","article-title":"Denoising of Diffusion MRI Data via Graph Framelet Matching in x-q Space","volume":"38","author":"Chen","year":"2019","journal-title":"IEEE Trans. Med Imaging"},{"key":"ref_43","first-page":"527","article-title":"Magnetic resonance imaging noise filtering using adaptive polynomial-fit non-local means","volume":"27","author":"Toa","year":"2019","journal-title":"Eng. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Yu, H., Ding, M., and Zhang, X. (2019). Laplacian Eigenmaps Network-Based Nonlocal Means Method for MR Image Denoising. Sensors, 19.","DOI":"10.3390\/s19132918"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Kim, K., Choi, J., and Lee, Y. (2020). Effectiveness of non-local means algorithm with an industrial 3 MeV LINAC high-energy X-ray sys-tem for non-destructive testing. Sensors, 20.","DOI":"10.3390\/s20092634"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.knosys.2015.02.029","article-title":"A local fuzzy thresholding methodology for multiregion image segmentation","volume":"83","author":"Curiale","year":"2015","journal-title":"Knowl. Based Syst."},{"key":"ref_47","unstructured":"Buades, A., Coll, B., and Morel, J.-M. (2005, January 20\u201325). A Non-Local Algorithm for Image Denoising. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Diego, CA, USA."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1570","DOI":"10.35940\/ijitee.L3131.1081219","article-title":"Image de-noising using optimized self similar patch based filter","volume":"8","author":"Gayathri","year":"2019","journal-title":"Int. J. Innov. Technol. Explor. Eng."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Bic, C., and Terebes, R. (2019, January 5\u20137). An improved NLM filter with increased noise robustness and adaptive similarity function. Proceedings of the 2019 IEEE 15th International Conference on Intelligent Computer Communication and Processing (ICCP), Cluj-Napoca, Romania.","DOI":"10.1109\/ICCP48234.2019.8959601"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1475","DOI":"10.1134\/S1064226918120070","article-title":"Fast Non-Local Mean Filter Algorithm Based on Recursive Calculation of Similarity Weights","volume":"63","author":"Karnaukhov","year":"2018","journal-title":"J. Commun. Technol. Electron."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Zhang, X., Hou, G., Ma, J., Yang, W., Lin, B., Xu, Y., Chen, W., and Feng, Y. (2014). Denoising MR Images Using Non-Local Means Filter with Combined Patch and Pixel Similarity. PLoS ONE, 9.","DOI":"10.1371\/journal.pone.0100240"},{"key":"ref_52","first-page":"171","article-title":"Rician Noise Removal by Non-Local Means Filtering for Low Signal-to-Noise Ratio MRI: Applications to DT-MRI","volume":"Volume 11","author":"Prima","year":"2008","journal-title":"Transactions on Petri Nets and Other Models of Concurrency XV"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1383","DOI":"10.1109\/TIP.2008.925382","article-title":"Noise and Signal Estimation in Magnitude MRI and Rician Distributed Images: A LMMSE Approach","volume":"17","author":"Westin","year":"2008","journal-title":"IEEE Trans. Image Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/12\/4161\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:17:46Z","timestamp":1760163466000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/12\/4161"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,17]]},"references-count":53,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["s21124161"],"URL":"https:\/\/doi.org\/10.3390\/s21124161","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,17]]}}}